We are pleased to announce that Andreas Rupp, professor at the Saarland University (Germany), will give the SFB 1313 "Pretty Porous Science Lecture" #68. His talk will be on "Hybrid finite element methods for PDEs in networks and hypergraphs".
Date: Tuesday, 18 November 2025
Time: 4 pm
Speaker: Prof. Dr. Andreas Rupp, Saarland University (Germany)
Title: "Hybrid finite element methods for PDEs in networks and hypergraphs"
Venue: Multi Media Lab (MML), U1.003, Pfaffenwaldring 61, 70569 Stuttgart, Campus Vaihingen. If you are interested in participating in the lecture online, please contact samaneh.vahiddastjerdi@mechbau.uni-stuttgart.de
Abstract
We introduce a general, analytical framework to express and to approximate partial differential equations (PDEs) numerically on graphs and networks of surfaces – generalized by the term hypergraphs. To this end, we consider PDEs on hypergraphs as singular limits of PDEs in networks of thin domains (such as fault planes, pipes, etc.), and we observe that (mixed) hybrid formulations offer useful tools to formulate such PDEs. Thus, our numerical framework is based on hybrid finite element methods (mainly the class of hybrid discontinuous Galerkin (HDG) methods).
In particular, we notice the beneficial properties of HDG in graphs and consider, as an example, the numerical solution of Timoshenko beam network models, comprised of Timoshenko beam equations on each edge of the network, which are coupled at the nodes of the network using rigid joint conditions. Our discretization of the beam network model achieves arbitrary orders of convergence under mesh refinement without increasing the size of the global system matrix. As a preconditioner for the typically very poorly conditioned global system matrix, we employ a two-level overlapping additive Schwarz method (if the graph is dense).
About Andreas Rupp
Andreas Rupp is a professor of Applied Mathematics at Saarland University (since September 2024), working in the Department of Mathematics in the Faculty of Mathematics and Computer Science. Before that, he was an Academy Research Fellow at Lappeenranta–Lahti University of Technology, focusing on uncertainty quantification for partial differential equations on hypergraphs, after serving as an Assistant Professor (tenure track) in Computational Engineering there. He earned his Ph.D. in Applied Mathematics (with a minor in soil science) from the University of Erlangen–Nuremberg in 2019.
His research interests lie in analysis and numerical methods for PDEs, especially in applications such as soil modeling and other environmental or physical systems—projects he has worked on include modelling soil microaggregates and large near-fractal pre-planetary dust aggregates. In addition to research and teaching, Andreas is active in organising scientific events and is connected with international research communities: he holds adjunct professorships at several Finnish universities, and is an invited member of the Young Academy Finland.